The government is considering abolishing a £20m grant that has helped the poorest pupils afford the cost of travelling to school, it emerged today.

Michael Gove, the education secretary, appearing before the Commons education select committee, also admitted there will not be a real-terms rise in school budgets, as he had previously claimed. The travel grant is given to pupils in primary and secondary schools and sixth-form colleges who cannot afford their daily bus fare or train journey. These pupils go to schools and colleges some distance from their homes for reasons of religious faith or to study particular subjects.

The grant will stop in its current form next summer, but the government is looking into how the funds can continue as part of its review into school transport.

A spokesman from the Department for Education said: "We are looking at what we can do and are determined that no child will lose out."

Yesterday, as part of England's school budget settlement, Gove said he would be reviewing home-to-school transport "so that we can better meet the needs of not only disadvantaged families, but all families, ensuring transport is properly targeted to those that need it most".

It emerged yesterday that school budgets in England will not now rise in real terms over the next four years. The chancellor, George Osborne, announced a 0.1% real-terms rise for schools in October's spending review. Surprised commentators said this was "his rabbit out of a hat". But it appears there will not be a real rise – ie a rise above inflation – in school budgets because of changes to the official inflation forecast.

This means that the funds given to schools for pupils whose parents are on less than a joint income of £16,000 a year will not, in real terms, be extra money. This funding, known as the pupil premium, is £430 for each poor pupil.

On the BBC's Andrew Marr Show last month Gove said the pupil premium would be new money from outside the schools budget.

Today, when MPs on the cross-party committee questioned Gove on the fact that there would not be a real-term rise in school budgets, he said it was because "growth had been faster and inflation was higher" than had been forecast.

"Economic forecasts come and go. It could be that in six months, they will be forecasting that inflation will have gone down, in which case we will get an increase bigger than 0.1%." He said local authorities were being given extra money to deal with a rise in pupil numbers.

He said he expected a rise in the number of families taking up free school meals for their children as a result of the pupil premium. All children who had received free school meals at any point in the last six years would be eligible for the pupil premium.

"We want to extend eligibility … a family that falls into poverty and then comes out of it will still be eligible for the pupil premium," he said.

Gove was pressed repeatedly over whether or not there would be real-term budget cuts for schools. "It is an incredibly difficult situation," he said. Asked by Labour's Bill Esterson if this meant cuts, Gove replied: "Yes. Well, it depends on the school."

But given the likely level of inflation, some institutions will face real-term cuts. "It will be tough for heads in the next year," Gove conceded. "Everything is being driven by the broader economic process – it is inescapable."

But he pledged more support to those wanting to become maths and science teachers in an effort to plug the current shortfall. "We will help pay off any student debt they have for as long as they are in teaching."

Andy Burnham, Labour's shadow education secretary, said that the combination of ending the travel grant and abolishing the education maintenance allowance (EMA) "could leave some of the poorest children and young people struggling to get to school or college".

The EMA is a grant that helps the poorest teenagers continue in education after they reach 16. It is being stopped at the end of next summer.

"Michael Gove is completely out of touch with the challenges facing poorer families – he is stacking the odds against aspirational young people who need a helping hand to succeed," Burnham said. "The coalition talks about social mobility, but they don't understand that it is schemes like these that provide the practical support that families need to get on in life."